Math July 13, 2026 · 8 Min Read

Base Converter Calculator – Guide & Formulas

Convert numbers instantly between custom bases from binary (base 2) up to base 36. Includes steps, division trees, and tables.

Convert any positive real number or integer from one custom base (radix) directly into another. Supports standard bases like Binary (2), Octal (8), Decimal (10), Hex (16), and arbitrary bases up to 36.

Key Takeaway

Use the free Base Converter Calculator to convert numbers instantly between custom bases from binary (base 2) up to base 36. includes steps, division trees, and tables. Get instant results with step-by-step explanations.

How to Use the Base Converter Calculator

  1. Enter the source number you wish to convert.
  2. Select its starting base (radix) and the target base you want to convert to.
  3. View the converted number alongside base-conversion arithmetic tables.

The Formula

Convert to decimal first: Sum(digit * base_from^pos). Then convert from decimal by successive division of base_to.

Variable Definitions

  • B_from: Original starting numeric base
  • B_to: The desired target numeric base

Converting 25 from Base 10 to Base 3 (Ternary)

Step-by-step conversion of integer 25 using successive division.

  1. Step 1: Divide 25 by 3: 25 / 3 = 8 with remainder 1.
  2. Step 2: Divide 8 by 3: 8 / 3 = 2 with remainder 2.
  3. Step 3: Divide 2 by 3: 2 / 3 = 0 with remainder 2.
  4. Step 4: Read the remainders from bottom to top: 221₃.

Frequently Asked Questions

What does base 36 mean?

Base 36 utilizes all ten digits (0-9) and all twenty-six letters of the English alphabet (A-Z) to represent numbers up to a value of 35 per single position.

Can this base converter handle fractional decimal points?

Yes, this converter is engineered to convert both whole integer parts and fractional components (e.g., 10.101₂ to decimal).

What is a radix?

Radix is simply another word for the "base" of a positional numeral system. For example, the decimal system has a radix of 10.